Qualifying conscience protections for institutions with requirements that they minimize hardship caused to the patient would prevent religious institutions from acting as a choke point on the path to services.
Navajo students whose beliefs forbid them from touching dead bodies need not forgo pursuing careers in medicine; some medical school administrators are teaching anatomy without cadavers.
Herman Melville's account of Bartleby the scrivener has something to teach us about the interactive nature of refusal and the empathy necessary for an exchange of values in the setting of conscientious refusal.